Informatics and Applications
2024, Volume 18, Issue 3, pp 45-51
TOWARDS A DEFINITION OF A BUSY PERIOD UNDER NONLOCAL DESCRIPTION OF INPUT FLOWS
Abstract
In course of a probabilistic modeling and analysis of complex controlled queueing systems with several
conflicting input flows, in a series of papers, an approach was successfully applied, one of its features being
a nonlocal description of various system building blocks. In this description, some information about true arrival
and leave times of customers is lost. It leads to difficulties in defining a busy period but that is one of classic
performance metrics for an operating queueing system. In this paper, a controlled queuing system busy period
definition is based on selecting those observation instants when queues reach zero level. A cyclic service algorithm
with fixed switching times as an example using a martingale technique and effective computational formulas are
obtained for the mathematical expectation of busy periods related to individual queues.
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[+] About this article
Title
TOWARDS A DEFINITION OF A BUSY PERIOD UNDER NONLOCAL DESCRIPTION OF INPUT FLOWS
Journal
Informatics and Applications
2024, Volume 18, Issue 3, pp 45-51
Cover Date
2024-09-20
DOI
10.14357/19922264240306
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
controlled queueing system; nonlocal description of blocks; nonordinary Poisson flows; cyclic service algorithm; busy period; multivariate denumerable Markov chain; martingale; generalized Rouche. s theorem; Lagrange interpolation polynomial
Authors
A. V. Zorine 
Author Affiliations
National Research Lobachevsky State University of Nizhny Novgorod, 23 Prosp. Gagarina, Nizhni Novgorod 603022, Russian Federation
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